Category notation

point of topological space are x,y, of a scheme are p,q..


Change Grp to abelian.
Whenever, you say tat there is a canonical morphism, state the property for which it would be unique.
Solve all ambiguous naming
Looks like the definition of P+(U)..P+(V) does not require all this mess.. try to define it.
Why does not one consider the limit instead of the colimit?
refer to the definition of product morphisms
make it coherent.
Would it be a presheaf..seperated..sheaf..where does it fail?
Make everything coherent.
Glenys.Wood@liverpool.ac.uk dental
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sheafiification
P+ is a presheaf.
+ is a functor.
We donot have to work out P+\righarrow Q+ explicitly in advance, but we need to show what it's afterwards
which particular morphism make it monomorphis...then sheaf

Colour the diagrams! mainly commutativity vertices
g_j to f_j j to i'

Examples of everything
Read it all. Consitance notation.
should I use U'j instead of Vj

goal of sheafifaction
universal property
application of having abelian category!!
Which is cech cohomology, H or H cech
pullback covering f^*\bcU using f_{1,1,}

Geometry is a topology space equipped with structure sheaf.

Embedding is a fully faithful functor.

Properness theorem
$\PR^19$ cubics in $\PR^3$.